MOISHEZON MANIFOLDS WITH NO NEF AND BIG CLASSES

Jia Jia; Sheng Meng

doi:10.1017/S0013091524000762

MOISHEZON MANIFOLDS WITH NO NEF AND BIG CLASSES

Jia Jia^*
, Sheng Meng

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We show that a compact complex manifold X has no non-trivial nef (1, 1)-classes if there is a non-biholomorphic bimeromorphic map f : X 99K Y , which is an isomorphism in codimension 1 to a compact Kähler manifold Y with h^1,1 = 1. In particular, there exist infinitely many isomorphic classes of smooth compact Moishezon threefolds with no nef and big (1, 1)-classes. This contradicts a recent paper (Strongly Jordan property and free actions of non-abelian free groups, Proc. Edinb. Math. Soc., 65(3) (2022), 736–746).

Original language	English
Pages (from-to)	198-204
Number of pages	7
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	68
Issue number	1
DOIs	https://doi.org/10.1017/S0013091524000762
State	Published - 1 Feb 2025

Keywords

Fujiki’s class C
Moishezon space
big
nef

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10.1017/S0013091524000762

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title = "MOISHEZON MANIFOLDS WITH NO NEF AND BIG CLASSES",

abstract = "We show that a compact complex manifold X has no non-trivial nef (1, 1)-classes if there is a non-biholomorphic bimeromorphic map f : X 99K Y , which is an isomorphism in codimension 1 to a compact K{\"a}hler manifold Y with h1,1 = 1. In particular, there exist infinitely many isomorphic classes of smooth compact Moishezon threefolds with no nef and big (1, 1)-classes. This contradicts a recent paper (Strongly Jordan property and free actions of non-abelian free groups, Proc. Edinb. Math. Soc., 65(3) (2022), 736–746).",

keywords = "Fujiki{\textquoteright}s class C, Moishezon space, big, nef",

author = "Jia Jia and Sheng Meng",

note = "Publisher Copyright: {\textcopyright} The Author(s), 2024.",

year = "2025",

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doi = "10.1017/S0013091524000762",

language = "英语",

volume = "68",

pages = "198--204",

journal = "Proceedings of the Edinburgh Mathematical Society",

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TY - JOUR

T1 - MOISHEZON MANIFOLDS WITH NO NEF AND BIG CLASSES

AU - Jia, Jia

AU - Meng, Sheng

N1 - Publisher Copyright: © The Author(s), 2024.

PY - 2025/2/1

Y1 - 2025/2/1

N2 - We show that a compact complex manifold X has no non-trivial nef (1, 1)-classes if there is a non-biholomorphic bimeromorphic map f : X 99K Y , which is an isomorphism in codimension 1 to a compact Kähler manifold Y with h1,1 = 1. In particular, there exist infinitely many isomorphic classes of smooth compact Moishezon threefolds with no nef and big (1, 1)-classes. This contradicts a recent paper (Strongly Jordan property and free actions of non-abelian free groups, Proc. Edinb. Math. Soc., 65(3) (2022), 736–746).

AB - We show that a compact complex manifold X has no non-trivial nef (1, 1)-classes if there is a non-biholomorphic bimeromorphic map f : X 99K Y , which is an isomorphism in codimension 1 to a compact Kähler manifold Y with h1,1 = 1. In particular, there exist infinitely many isomorphic classes of smooth compact Moishezon threefolds with no nef and big (1, 1)-classes. This contradicts a recent paper (Strongly Jordan property and free actions of non-abelian free groups, Proc. Edinb. Math. Soc., 65(3) (2022), 736–746).

KW - Fujiki’s class C

KW - Moishezon space

KW - big

KW - nef

UR - https://www.scopus.com/pages/publications/85210385877

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DO - 10.1017/S0013091524000762

M3 - 文章

AN - SCOPUS:85210385877

SN - 0013-0915

VL - 68

SP - 198

EP - 204

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

IS - 1

ER -

MOISHEZON MANIFOLDS WITH NO NEF AND BIG CLASSES

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Keywords

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